I think the issue with vector using twice as much of memory is when you keep making push_back's causing it to run out of memory, so it allocates more memory by a factor of 2 or something like that

After seeing so many people writing that they should use $$$4 \cdot 10^6$$$ integers(the main reason I could find for this phenomenon is cp-algorithms's segment tree making an array of size $$$4 \cdot N$$$) for segment tree in this problem I felt the need to write this.

Let $$$M$$$ be the smallest power of $$$2$$$ greater than $$$N$$$. Then, if you want the $$$O(n)$$$ initialization with 1 for loop(for (int i=M-1;i>=1;--i) seg[i]=seg[i*2]+seg[i*2+1];) you should have an array of size $$$2 \cdot M$$$(which is in the worst case $$$4 \cdot N$$$, but if $$$N=10^5$$$ or $$$2 \cdot 10^5$$$ then $$$M$$$ is about $$$1.3 \cdot N$$$; if $$$N=5 \cdot 10^5$$$ or $$$10^6$$$ then $$$M$$$ is about $$$1.05 \cdot N$$$, so in most problems the amount of memory you need isn't that much bigger than $$$2 \cdot N$$$).

If you don't need the $$$O(n)$$$ initialization with 1 for loop you should have an array of size $$$M+N$$$(which is in the worst case $$$3 \cdot N$$$, but as demonstrated above it's usually not).

In my implementation of segment tree $$$M$$$ is necessary for both update and query, so unless there's some segment tree implementation that I don't know of which doesn't require $$$M$$$ and doesn't use $$$2 \cdot N$$$ memory I see no reason for a person to use $$$4 \cdot 10^6$$$ integers in a segment tree with $$$N = 10^6$$$.